[QUE/QFT-15008] QFT-PROBLEM

\(\newcommand{\dd}[2][]{\frac{d #1}{d #2}}\)
Assuming \(\frac{g}{4!} \pi^4(x)\) interaction for neutral pions of mass \(m\), find

• transition probability per unit time per unit volume for \(\pi - \pi\) scattering.
• Compute the total cross section for the scattering process and show that \[ \dd[\sigma]{\Omega}= \frac{g^2}{64\pi^2 E_\text{cm}^2}\]